Compute the flux of the vector field $ { \vec { F } } = ( x - 4 y ) \vec { i } + ( 4 y - 2 z ) \vec { j } + 5 x \vec { k }$ through the surface S, where S is the part of the plane z = x + 2y above the rectangle $0 \leq x \leq 2,0 \leq y \leq 3$ oriented upward.

Question

Compute the flux of the vector field $  { \vec { F } } = ( x - 4 y ) \vec { i } + ( 4 y - 2 z ) \vec { j } + 5 x \vec { k }$ through the surface S, where S is the part of the plane z = x + 2y above the rectangle $0 \leq x \leq 2,0 \leq y \leq 3$ oriented upward.

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The Answer of Compute the flux of the vector field $  { \vec { F } } = ( x - 4 y ) \vec { i } + ( 4 y - 2 z ) \vec { j } + 5 x \vec { k }$ through the surface S, where S is the part of the plane z = x + 2y above the rectangle $0 \leq x \leq 2,0 \leq y \leq 3$ oriented upward.

Compute the Flux of the Vector Field F⃗=(x−4y)i⃗+(4y−2z)j⃗+5xk⃗ { \vec { F } } = ( x - 4 y ) \vec { i } + ( 4 y - 2 z ) \vec { j } + 5 x \vec { k }F=(x−4y)i+(4y−2z)j​+5xk

Compute the Flux of the Vector Field ${ \vec { F } } = ( x - 4 y ) \vec { i } + ( 4 y - 2 z ) \vec { j } + 5 x \vec { k }$